Hello,

I'll show you the way one of my teacher taught us

We'll keep your hypothesis.

Make a word this way :

Do you agree that there are letters a ?

Plus, there are letters b (I'll let you do the counting).

Therefore, this word has letters.

So we're looking for all words of letters and containing k letters a and n-1 letters b.

This is the part you have to understand : it's equivalent to finding the possible places where b can be.

So this is the combinations of (p-1) among k+(n-1)..

If I have time, I'll try to post an example...